The main result of this work is given in Fig. (REF ), the spectral density of GW today for a model of quartic chaotic warm inflation. Those are induced at second order by the enhancement of the primordial spectrum of curvature perturbations. In warm inflation we have a coupled, resonant system of inflaton and radiation perturbations, and when dissipation \(\Upsilon \)  grows with the \(T\)  of the thermal bath, this gives rise to the amplification of the primordial perturbations [1]}, [2]}. When this effect already takes place at CMB scales, it may lead to a blue-tilted primordial spectrum excluded by observations. To avoid this, we have focused on the SLWI model [3]}, a variant of the LWI model with an inverse \(T\)  dependent dissipative coefficient at CMB scales, due to the coupling of the inflaton to a pair of light scalars. However, as inflation proceeds, scalar masses become larger than \(T\) , and we recover a model with \(\Upsilon \)  growing with \(T\) , and a spectrum that is naturally enhanced by the end of inflation. We combine this with a quartic chaotic potential, instead of the quadratic one studied in [3]}: while a quadratic potential is compatible with observations when the system is already in the SDR \(50-60\)  efolds before the end, the amplification experience by the spectrum upto the end of inflation is larger in the quartic model.
